An arc of lemgth 28cm subtends an angle at the centre of a circle. In the same circle, what angle does an arc of length 35 subtend
original angle * (35/28)
To find the angle subtended by an arc in a circle, we can use the formula:
Angle = (Arc Length / Circumference) * 360 degrees
First, let's find the circumference of the circle. The formula for the circumference is:
Circumference = 2 * π * radius
However, we are not given the radius of the circle. But since we know the length of the arc and the angle at the center of the circle, we can use them to find the radius.
Given the length of the first arc is 28 cm, and it subtends an angle at the center, let's call it θ1.
Using the formula for the length of an arc:
Arc Length = (θ1 / 360 degrees) * Circumference
Substituting the given values, we get:
28 cm = (θ1 / 360 degrees) * Circumference
Now, let's find the circumference using the second arc length and the previously derived value of the circumference.
Given the length of the second arc is 35 cm, and it subtends an angle at the center, let's call it θ2.
Using the formula for the length of an arc:
35 cm = (θ2 / 360 degrees) * Circumference
We can rearrange these equations to solve for the common value of the circumference:
θ1 / 360 degrees = 28 cm / Circumference
θ2 / 360 degrees = 35 cm / Circumference
Now we can equate the two equations to find the angle θ2:
(θ2 / 360 degrees) = (35 cm / Circumference)
Substituting the value for θ1 / 360 degrees from the first equation, we get:
(θ2 / 360 degrees) = (35 cm / (28 cm / (θ1 / 360 degrees)))
Simplifying the equation, we have:
(θ2 / 360 degrees) = (35 / 28) * (θ1 / 360 degrees)
Now, we can solve for θ2:
θ2 = (35 / 28) * θ1
So, the angle subtended by the arc of length 35 cm is (35 / 28) times the angle subtended by the arc of length 28 cm.